your first question is too broad. we use it because it works. there are scenarios where you will use set_case_analysis for things other than scan. I am taping out a design right now that has 4 functional corners and a couple of case analysis statements for some "enable" signals.
"closing time with multiple sdcs" is technically not correct. you close timing on multiple corners, functional or process corners, which may or may not include multiple sdcs. as long as you have all the corners you care about set to active, the tools will work on ALL of them at the same time.